A class of transformed joint quantile time series models with applications to health studies

Extensions of quantile regression modeling for time series analysis are extensively employed in medical and health studies. This study introduces a specific class of transformed quantile-dispersion regression models for non-stationary time series. These models possess the flexibility to incorporate the time-varying structure into the model specification, enabling precise predictions for future decisions. Our proposed modeling methodology applies to dynamic processes characterized by high variation and possible periodicity, relying on a non-linear framework. Additionally, unlike the transformed time series model, our approach directly interprets the regression parameters concerning the initial response. For computational purposes, we present an iteratively reweighted least squares algorithm. To assess the performance of our model, we conduct simulation experiments. To illustrate the modeling strategy, we analyze time-series measurements of influenza infection and daily COVID-19 deaths.